We investigate the representations of the hyperalgebras associated to the map algebras [Formula: see text], where [Formula: see text] is any finite-dimensional complex simple Lie algebra and [Formula: see text] is any associative commutative unitary algebra with a multiplicatively closed basis. We consider the natural definition of the local and global Weyl modules, and the Weyl functor for these algebras. Under certain conditions, we prove that these modules satisfy certain universal properties, and we also give conditions for the local or global Weyl modules to be finite-dimensional or finitely generated, respectively.

中文翻译：

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超映射代数的外尔模块和外尔函子

我们研究了与地图代数 [Formula: see text] 相关联的超代数的表示，其中 [Formula: see text] 是任何有限维复简单李代数， [Formula: see text] 是任何具有 a乘法闭基。我们考虑局部和全局外尔模块的自然定义，以及这些代数的外尔函子。在一定条件下，我们证明了这些模块满足一定的普遍性质，我们还给出了局部或全局 Weyl 模块分别是有限维或有限生成的条件。